Sure, let's find the total surface area of the regular square pyramid step-by-step given the base area and slant height.
1. Find the side length of the base:
The base of a regular square pyramid is a square. So, if the area of the base is 25 cm², we can find the side length of the square by taking the square root of the area.
[tex]\[
\text{Side length} = \sqrt{\text{Base area}} = \sqrt{25 \text{ cm}^2} = 5 \text{ cm}
\][/tex]
2. Calculate the area of one triangular face:
The pyramid has 4 triangular faces, and since it’s a regular square pyramid, each triangular face is an isosceles triangle with the base being the side length of the square base, and the height being the slant height of the pyramid.
[tex]\[
\text{Triangular face area} = \frac{1}{2} \times \text{Side length} \times \text{Slant height} = \frac{1}{2} \times 5 \text{ cm} \times 8 \text{ cm} = 20 \text{ cm}^2
\][/tex]
3. Calculate the total surface area:
The total surface area of the pyramid is the sum of the base area and the total area of the 4 triangular faces.
[tex]\[
\text{Total surface area} = \text{Base area} + 4 \times \text{Triangular face area} = 25 \text{ cm}^2 + 4 \times 20 \text{ cm}^2 = 25 \text{ cm}^2 + 80 \text{ cm}^2 = 105 \text{ cm}^2
\][/tex]
Thus, the total surface area of the regular square pyramid is [tex]\( \boxed{105} \)[/tex] cm².
So the correct answer is:
B. 105 cm²
